As far as I can make out, a tuning box can only alter the amount of fuel and the timing of the fuel injection. Unlike a remap, it cannot change the fuel pressure. So from your thoughts Carlosmatey, the remap is going to give the ticking time bomb with the fuel pump.

Tuning box cannot do this.

As for over fueling, both methods increase the fuel at given times to achieve the extra HP.

Unless someone knows different......

Sh*t. Late for another appointment. Watch has stopped ticking.
OMG. Where IS that ticking sound coming from?

A tuning box works in only one way. It plugs in between the fuel rail and fuel rail pressure sensor. It then fools the signal back to the main injection pump that the pump is running at a low pressure so pushes the pump pressure up. This injects more fuel, simple. It cannot adjust injection timing, turbo pressure, torque limiters, top speed limiter ect ect.

It can shorten the life of the pump due to the higher pressure and the injectors can fail due to the higher pressure at the back on the injectors. A remap, depending who written the mapping does NOT increase fuel rail pressure, more fuel is injected by opening the injectors longer and more advance on the injection timing.